
"""simple docstring"""


import torch
from torch import nn




class  __lowerCamelCase  ( nn.Module			):




				def __init__(				self							,						UpperCAmelCase							,						UpperCAmelCase							,						UpperCAmelCase							,						UpperCAmelCase							,						UpperCAmelCase=1							,						UpperCAmelCase=False   ):
							super().__init__()

							lowerCamelCase_					=  n_token
							lowerCamelCase_					=  d_embed
							lowerCamelCase_					=  d_proj

							lowerCamelCase_					=  cutoffs + [n_token]
							lowerCamelCase_					=  [0] + self.cutoffs
							lowerCamelCase_					=  div_val

							lowerCamelCase_					=  self.cutoffs[0]
							lowerCamelCase_					=  len(self.cutoffs   ) - 1
							lowerCamelCase_					=  self.shortlist_size + self.n_clusters

							if self.n_clusters > 0:
										lowerCamelCase_					=  nn.Parameter(torch.zeros(self.n_clusters							,						self.d_embed   )   )
										lowerCamelCase_					=  nn.Parameter(torch.zeros(self.n_clusters   )   )

							lowerCamelCase_					=  nn.ModuleList()
							lowerCamelCase_					=  nn.ParameterList()

							if div_val == 1:
										for i in range(len(self.cutoffs   )   ):
													if d_proj != d_embed:
																self.out_projs.append(nn.Parameter(torch.FloatTensor(UpperCAmelCase							,						UpperCAmelCase   )   )   )
													else:
																self.out_projs.append(UpperCAmelCase   )

										self.out_layers.append(nn.Linear(UpperCAmelCase							,						UpperCAmelCase   )   )
							else:
										for i in range(len(self.cutoffs   )   ):
													lowerCamelCase_		, lowerCamelCase_					=  self.cutoff_ends[i], self.cutoff_ends[i + 1]
													lowerCamelCase_					=  d_embed // (div_val**i)

													self.out_projs.append(nn.Parameter(torch.FloatTensor(UpperCAmelCase							,						UpperCAmelCase   )   )   )

													self.out_layers.append(nn.Linear(UpperCAmelCase							,						r_idx - l_idx   )   )

							lowerCamelCase_					=  keep_order




				def        UpperCAmelCase__						(				self							,						UpperCAmelCase							,						UpperCAmelCase							,						UpperCAmelCase							,						UpperCAmelCase   ):
							if proj is None:
										lowerCamelCase_					=  nn.functional.linear(UpperCAmelCase							,						UpperCAmelCase							,						bias=UpperCAmelCase   )
							else:
										# if CUDA_MAJOR <= 9 and CUDA_MINOR <= 1:
										lowerCamelCase_					=  nn.functional.linear(UpperCAmelCase							,						proj.t().contiguous()   )
										lowerCamelCase_					=  nn.functional.linear(UpperCAmelCase							,						UpperCAmelCase							,						bias=UpperCAmelCase   )
										# else:
										#     logit = torch.einsum('bd,de,ev->bv', (hidden, proj, weight.t()))
										#     if bias is not None:
										#         logit = logit + bias

							return logit




				def        UpperCAmelCase__						(				self							,						UpperCAmelCase							,						UpperCAmelCase=None							,						UpperCAmelCase=False   ):

							if labels is not None:
										# Shift so that tokens < n predict n
										lowerCamelCase_					=  hidden[..., :-1, :].contiguous()
										lowerCamelCase_					=  labels[..., 1:].contiguous()
										lowerCamelCase_					=  hidden.view(-1							,						hidden.size(-1   )   )
										lowerCamelCase_					=  labels.view(-1   )
										if hidden.size(0   ) != labels.size(0   ):
													raise RuntimeError('''Input and labels should have the same size in the batch dimension.'''   )
							else:
										lowerCamelCase_					=  hidden.view(-1							,						hidden.size(-1   )   )

							if self.n_clusters == 0:
										lowerCamelCase_					=  self._compute_logit(UpperCAmelCase							,						self.out_layers[0].weight							,						self.out_layers[0].bias							,						self.out_projs[0]   )
										if labels is not None:
													lowerCamelCase_					=  labels != -100
													lowerCamelCase_					=  torch.zeros_like(UpperCAmelCase							,						dtype=hidden.dtype							,						device=hidden.device   )
													lowerCamelCase_					=  (
													    -nn.functional.log_softmax(UpperCAmelCase							,						dim=-1   )[mask].gather(1							,						labels[mask].unsqueeze(1   )   ).squeeze(1   )
													)
										else:
													lowerCamelCase_					=  nn.functional.log_softmax(UpperCAmelCase							,						dim=-1   )
							else:
										# construct weights and biases
										lowerCamelCase_		, lowerCamelCase_					=  [], []
										for i in range(len(self.cutoffs   )   ):
													if self.div_val == 1:
																lowerCamelCase_		, lowerCamelCase_					=  self.cutoff_ends[i], self.cutoff_ends[i + 1]
																lowerCamelCase_					=  self.out_layers[0].weight[l_idx:r_idx]
																lowerCamelCase_					=  self.out_layers[0].bias[l_idx:r_idx]
													else:
																lowerCamelCase_					=  self.out_layers[i].weight
																lowerCamelCase_					=  self.out_layers[i].bias

													if i == 0:
																lowerCamelCase_					=  torch.cat([weight_i, self.cluster_weight]							,						dim=0   )
																lowerCamelCase_					=  torch.cat([bias_i, self.cluster_bias]							,						dim=0   )

													weights.append(UpperCAmelCase   )
													biases.append(UpperCAmelCase   )

										lowerCamelCase_		, lowerCamelCase_		, lowerCamelCase_					=  weights[0], biases[0], self.out_projs[0]

										lowerCamelCase_					=  self._compute_logit(UpperCAmelCase							,						UpperCAmelCase							,						UpperCAmelCase							,						UpperCAmelCase   )
										lowerCamelCase_					=  nn.functional.log_softmax(UpperCAmelCase							,						dim=1   )

										if labels is None:
													lowerCamelCase_					=  hidden.new_empty((head_logit.size(0   ), self.n_token)   )
										else:
													lowerCamelCase_					=  torch.zeros_like(UpperCAmelCase							,						dtype=hidden.dtype							,						device=hidden.device   )

										lowerCamelCase_					=  0
										lowerCamelCase_					=  [0] + self.cutoffs
										for i in range(len(UpperCAmelCase   ) - 1   ):
													lowerCamelCase_		, lowerCamelCase_					=  cutoff_values[i], cutoff_values[i + 1]

													if labels is not None:
																lowerCamelCase_					=  (labels >= l_idx) & (labels < r_idx)
																lowerCamelCase_					=  mask_i.nonzero().squeeze()

																if indices_i.numel() == 0:
																			continue

																lowerCamelCase_					=  labels.index_select(0							,						UpperCAmelCase   ) - l_idx
																lowerCamelCase_					=  head_logprob.index_select(0							,						UpperCAmelCase   )
																lowerCamelCase_					=  hidden.index_select(0							,						UpperCAmelCase   )
													else:
																lowerCamelCase_					=  hidden

													if i == 0:
																if labels is not None:
																			lowerCamelCase_					=  head_logprob_i.gather(1							,						target_i[:, None]   ).squeeze(1   )
																else:
																			lowerCamelCase_					=  head_logprob[:, : self.cutoffs[0]]
													else:
																lowerCamelCase_		, lowerCamelCase_		, lowerCamelCase_					=  weights[i], biases[i], self.out_projs[i]

																lowerCamelCase_					=  self._compute_logit(UpperCAmelCase							,						UpperCAmelCase							,						UpperCAmelCase							,						UpperCAmelCase   )
																lowerCamelCase_					=  nn.functional.log_softmax(UpperCAmelCase							,						dim=1   )
																lowerCamelCase_					=  self.cutoffs[0] + i - 1  # No probability for the head cluster
																if labels is not None:
																			lowerCamelCase_					=  head_logprob_i[:, cluster_prob_idx] + tail_logprob_i.gather(
																			    1							,						target_i[:, None]   ).squeeze(1   )
																else:
																			lowerCamelCase_					=  head_logprob[:, cluster_prob_idx, None] + tail_logprob_i
																			lowerCamelCase_					=  logprob_i

													if labels is not None:
																if (hasattr(self							,						'''keep_order'''   ) and self.keep_order) or keep_order:
																			out.index_copy_(0							,						UpperCAmelCase							,						-logprob_i   )
																else:
																			out[offset : offset + logprob_i.size(0   )].copy_(-logprob_i   )
																offset += logprob_i.size(0   )

							return out





				def        UpperCAmelCase__						(				self							,						UpperCAmelCase   ):
							if self.n_clusters == 0:
										lowerCamelCase_					=  self._compute_logit(UpperCAmelCase							,						self.out_layers[0].weight							,						self.out_layers[0].bias							,						self.out_projs[0]   )
										return nn.functional.log_softmax(UpperCAmelCase							,						dim=-1   )
							else:
										# construct weights and biases
										lowerCamelCase_		, lowerCamelCase_					=  [], []
										for i in range(len(self.cutoffs   )   ):
													if self.div_val == 1:
																lowerCamelCase_		, lowerCamelCase_					=  self.cutoff_ends[i], self.cutoff_ends[i + 1]
																lowerCamelCase_					=  self.out_layers[0].weight[l_idx:r_idx]
																lowerCamelCase_					=  self.out_layers[0].bias[l_idx:r_idx]
													else:
																lowerCamelCase_					=  self.out_layers[i].weight
																lowerCamelCase_					=  self.out_layers[i].bias

													if i == 0:
																lowerCamelCase_					=  torch.cat([weight_i, self.cluster_weight]							,						dim=0   )
																lowerCamelCase_					=  torch.cat([bias_i, self.cluster_bias]							,						dim=0   )

													weights.append(UpperCAmelCase   )
													biases.append(UpperCAmelCase   )

										lowerCamelCase_		, lowerCamelCase_		, lowerCamelCase_					=  weights[0], biases[0], self.out_projs[0]
										lowerCamelCase_					=  self._compute_logit(UpperCAmelCase							,						UpperCAmelCase							,						UpperCAmelCase							,						UpperCAmelCase   )

										lowerCamelCase_					=  hidden.new_empty((head_logit.size(0   ), self.n_token)   )
										lowerCamelCase_					=  nn.functional.log_softmax(UpperCAmelCase							,						dim=1   )

										lowerCamelCase_					=  [0] + self.cutoffs
										for i in range(len(UpperCAmelCase   ) - 1   ):
													lowerCamelCase_		, lowerCamelCase_					=  cutoff_values[i], cutoff_values[i + 1]

													if i == 0:
																lowerCamelCase_					=  head_logprob[:, : self.cutoffs[0]]
													else:
																lowerCamelCase_		, lowerCamelCase_		, lowerCamelCase_					=  weights[i], biases[i], self.out_projs[i]

																lowerCamelCase_					=  self._compute_logit(UpperCAmelCase							,						UpperCAmelCase							,						UpperCAmelCase							,						UpperCAmelCase   )
																lowerCamelCase_					=  nn.functional.log_softmax(UpperCAmelCase							,						dim=1   )

																lowerCamelCase_					=  head_logprob[:, -i] + tail_logprob_i
																lowerCamelCase_					=  logprob_i

										return out








'''simple docstring'''



import os

lowerCAmelCase_  :							Union[str, Any]             =    {'I': 1, 'V': 5, 'X': 10, 'L': 50, 'C': 100, 'D': 500, 'M': 1000}
def        UpperCAmelCase (    A	:					str					):
							SCREAMING_SNAKE_CASE       :   str         =      0

							SCREAMING_SNAKE_CASE       :   List[str]         =      0
							while index < len(A					) - 1:
														SCREAMING_SNAKE_CASE       :   Dict         =      SYMBOLS[numerals[index]]
														SCREAMING_SNAKE_CASE       :   str         =      SYMBOLS[numerals[index + 1]]
														if current_value < next_value:
																					total_value -= current_value
														else:
																					total_value += current_value
														index += 1
							total_value += SYMBOLS[numerals[index]]

							return total_value
def        UpperCAmelCase (    A	:					int					):
							SCREAMING_SNAKE_CASE       :   Any         =      ''''''

							SCREAMING_SNAKE_CASE       :   Dict         =      num // 1000
							numerals += m_count * "M"
							num %= 1000

							SCREAMING_SNAKE_CASE       :   str         =      num // 100
							if c_count == 9:
														numerals += "CM"
														c_count -= 9
							elif c_count == 4:
														numerals += "CD"
														c_count -= 4
							if c_count >= 5:
														numerals += "D"
														c_count -= 5
							numerals += c_count * "C"
							num %= 100

							SCREAMING_SNAKE_CASE       :   Any         =      num // 10
							if x_count == 9:
														numerals += "XC"
														x_count -= 9
							elif x_count == 4:
														numerals += "XL"
														x_count -= 4
							if x_count >= 5:
														numerals += "L"
														x_count -= 5
							numerals += x_count * "X"
							num %= 10

							if num == 9:
														numerals += "IX"
														num -= 9
							elif num == 4:
														numerals += "IV"
														num -= 4
							if num >= 5:
														numerals += "V"
														num -= 5
							numerals += num * "I"

							return numerals
def        UpperCAmelCase (    A	:					str = "/p089_roman.txt"					):
							SCREAMING_SNAKE_CASE       :   List[str]         =      0

							with open(os.path.dirname(A					) + roman_numerals_filename					) as filea:
														SCREAMING_SNAKE_CASE       :   str         =      filea.readlines()

							for line in lines:
														SCREAMING_SNAKE_CASE       :   Any         =      line.strip()
														SCREAMING_SNAKE_CASE       :   Union[str, Any]         =      parse_roman_numerals(A					)
														SCREAMING_SNAKE_CASE       :   Any         =      generate_roman_numerals(A					)
														savings += len(A					) - len(A					)

							return savings


if __name__ == "__main__":
							print(f'{solution() = }')




